Question

Krystal’s poster project for reading class is 2 feet high and 1 1 2 feet wide. Her friend Victoria’s poster is 4 feet high and 1 1 2 feet wide. How many times larger is the area of Victoria’s poster? Draw a model on the grid paper, and show your multiplication work here.

Answer 1

The area of Victoria's poster is twice the area of Krystal's poster.

How compare the areas of two similar posters

The two areas are shown in the image attached below. Each poster represents a rectangle and the ratio between the two areas ($r_{A}$), no unit, is defined by the following formula:

$r_{A} = \frac{w_{V}\cdot h_{V}}{w_{K}\cdot h_{K}}$     (1)

Where:

• $w_{V}$ - Width of Victoria's poster, in feet.
• $h_{V}$ - Height of Victoria's poster, in feet.
• $w_{K}$ - Width of Krystal's poster, in feet.
• $h_{K}$ - Height of Krystal's poster, in feet.

If we know that $h_{V} = 4\,ft$, $w_{V} = 1.5\,ft$, $h_{K} = 2\,ft$ and $w_{K} = 1.5\,ft$, then the ratio between the two areas is:

$r_{A} = \frac{(4)\cdot (1.5)}{(2)\cdot (1.5)}$

$r_{A} = 2$

The area of Victoria's poster is twice the area of Krystal's poster. $\blacksquare$

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